On the PID-structured model-free adaptive control: a comparison of different approaches

In this paper, a PID-structured controller with time-varying gains is introduced using model-free adaptive control (MFAC) methodologies. The MFAC uses a control-oriented linearized data-model to produce control input only using input/output (I/O) data of the system. One of the data-model structures is full form dynamic linearization (FFDL), which considers the effect of a time-window of previous I/O in the linearized model. A specific I/O window length in FFDL leads to a MFAC controller whose structure is similar to discrete multivariable type PID. By manipulating the control objective function, however, similar PID-structured (PIDs) controller can be realized using a less sophisticated data-model exploiting the compact form dynamic linearization (CFDL) technique. The complexity of the new PIDsMFAC-CFDL and the one realized by MFAC-FFDL are compared in terms of the total number of adjustable parameters when dealing with MIMO systems. The controllers are also applied on a simulated model of a nonlinear MIMO three-tank system (3TS). The results demonstrate that the number of parameters to be tuned can decrease heavily by considering the new approach. In addition, PIDsMFAC-CFDL delivers a smooth transition toward the given reference with less error and less consumed energy.